Solve for $x$ and $y$ using elimination. ${-6x-y = -16}$ ${-5x+y = 5}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-11x = -11$ $\dfrac{-11x}{{-11}} = \dfrac{-11}{{-11}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {-6x-y = -16}\thinspace$ to find $y$ ${-6}{(1)}{ - y = -16}$ $-6-y = -16$ $-6{+6} - y = -16{+6}$ $-y = -10$ $\dfrac{-y}{{-1}} = \dfrac{-10}{{-1}}$ ${y = 10}$ You can also plug ${x = 1}$ into $\thinspace {-5x+y = 5}\thinspace$ and get the same answer for $y$ : ${-5}{(1)}{ + y = 5}$ ${y = 10}$